class: center, middle, inverse, title-slide .title[ #
4 (3) years later: A look back at the sport climbing competition format and scoring system at Tokyo 2020 (2021)
] .subtitle[ ## Quang Nguyen ] .institute[ ### UCSAS 2024 ] .date[ ###
qntkhvn   Â
@qntkhvn
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qntkhvn.netlify.app ] --- class: center, middle <p style="font-size:3.8em"> <b> Sport Climbing at Tokyo 2020 </b> </p> --- # Competition & Scoring - Sport climbing made its Olympic debut at Tokyo 2020 - 3 disciplines: speed climbing, bouldering, lead climbing - Only 1 set of medals for each gender at the Olympics - Combined scoring system: multiplying 3 disciplines' ranks (best score = lowest score) - Example: `\(1\)`st in speed `\(\times\)` `\(5\)`th in bouldering `\(\times\)` `\(7\)`th in lead `\(=\)` total score of `\(35\)` - 2 rounds: qualification (20 climbers), final (top 8 from qualification) --- # Concerns * Climber interviews with Climbing Magazine in 2016: > "I am NOT in support of the format that imposes that all climbers must compete in speed climbing. That is like asking a middle distance runner to compete in the sprint. Speed climbing is a sport within our sport." - Lynn Hill, former US Climber. > "Honestly, the people that will suffer the most are the ones that focus only on speed climbing. Those skills/abilities don’t transfer as well to the other disciplines." - Mike Doyle, US Climber. * Words and phrases: "bogus", "a bummer", "less than ideal", "not in support", "cheesy and unfair". --- # Investigation Questions **What are the properties and limitations of the sport climbing "triathlon" format and rank-product scoring?** * What are the probabilities of qualifying/winning, given certain placements? * What are the expected placement scores for each round? * Are the concerns of the climbers valid? --- class: center, middle <p style="font-size:3.8em"> <b> Simulation Study </b> </p> --- # Assumptions * Within-discipline uniform ranks * Between-discipline correlation * Simulate from a calibrated copula with a specified dependence structure * Incorporate correlation (Kendall's `\(\tau\)`) between bouldering and lead obtained from empirical data * Speed is assumed independent of bouldering and lead --- # Simulation results: Win Probability vs Correlation <!-- Win probability given a victory in **speed** vs in **bouldering or lead** for different correlation values --> <!-- <div style="height:-100px;"</div> --> .pull-left[ As bouldering-lead correlation increases, the overall win probability * increases, given a boulder/lead victory * decreases, given a speed victory When bouldering and lead are perfectly correlated, the gold medal probability * only ~20.5% for winning speed * ~90.3% for winning boulder/lead ] <!-- a speed winner only has a 20.5% of winning a gold medal --> <!-- winning boulder/lead brings about a 90.3% chance of an overall first place finish --> .pull-right[ <img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-1-1.png" width="504" style="display: block; margin: auto;" /> ] --- # Simulation results: Placement Probabilities .pull-left[ Given that a climber wins any discipline... * For a qualifier, what is the probability of qualifying for final (finishing at 8 or better)? `\(99.5\%\)` * For a finalist, what is the probability of winning a medal (finishing in top 3)? `\(84.8\%\)` ] .pull-right[ <img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-2-1.png" width="504" style="display: block; margin: auto;" /> ] --- # Simulation results: Placement Scores .pull-left[ * Average target scores * For qualifiers: `\(453\)` to make top `\(8\)` * For finalists: `\(9, 19, 33\)` to win gold, silver, bronze ] .pull-right[ <img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-3-1.png" width="504" style="display: block; margin: auto;" /> ] --- class: center, middle <p style="font-size:3.8em"> <b> Correlation Analysis </b> </p> --- # Rank Correlation - Correlations between the overall rank and the ranks of the individual disciplines (speed, bouldering, and lead) - Case study: Tokyo 2020 Women's Qualification
climber
overall
speed
bouldering
lead
Janja Garnbret
1
14
1
4
Seo Chae-hyun
2
17
5
1
Miho Nonaka
3
4
8
3
Akiyo Noguchi
4
9
3
6
Brooke Raboutou
5
12
2
8
--- # Rank Correlation **Lead** and **bouldering** ranks are more highly correlated with **overall** rank than **speed**. .pull-left[ <img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-6-1.png" width="612" style="display: block; margin: auto;" /> ] .pull-right[ <br>
Discipline
Kendall
p-value
Bootstrapped 95% CI
Speed
0.147
0.386
(−0.191, 0.469)
Bouldering
0.432
0.007
(0.107, 0.691)
Lead
0.463
0.004
(0.112, 0.753)
] --- # Principal component analysis .pull-left[ - Visualize underlying correlations that exist among the climbing discipline performances - Speed race time - Bouldering tops - Lead holds ] .pull-right[ - Case study: Tokyo 2020 Women's Qualification
climber
speed_time
bould_tops
lead_holds
Janja Garnbret
9.44
4
30.0
Seo Chae-hyun
10.01
2
40.5
Miho Nonaka
7.55
1
30.5
Akiyo Noguchi
8.23
3
27.5
Brooke Raboutou
8.67
3
26.5
Jessica Pilz
8.51
1
33.5
Aleksandra Mirosław
6.97
0
12.0
] --- # Principal component analysis .pull-left[ * Strong and positive correlation between bouldering and lead performances * Speed time is completely separated from other two performance variables **The competition format is stacked against speed climbers** ] .pull-right[ <img src="data:image/png;base64,#pca.png" width="688" style="display: block; margin: auto;" /> ] --- class: center, middle <p style="font-size:3.8em"> <b> Leave-one-climber-out Analysis </b> </p> --- # Independence of irrelevant alternatives **What would happen to the overall rankings (in particular, order of medalists) if one climber got disqualified?** <!-- - Independence of irrelevant alternatives (IIA) --> <!-- - After a winner is determined, if one of the losing candidates drops out and the votes are recounted, there should not be a change in the winner --> <!-- - We have evidence for a violation of the IIA property from real data. --> - This has a connection with the independence of irrelevant alternatives (IIA) - IIA: rank orderings should not change if a losing candidate is removed and the scores are re-calculated - There's evidence for a violation of the IIA property from real data. --- # IIA Violation Panel 5: If 5th-place climber (Krasovskaia) was excluded, climber with actual rank 4 (Meul) would move up to 2nd!!! <img src="data:image/png;base64,#climbing_ucsas_files/figure-html/unnamed-chunk-12-1.png" width="648" style="display: block; margin: auto;" /> --- class: center, middle <p style="font-size:3.8em"> <b> Takeaways </b> </p> --- # Discussion - The idea of a climbing triathlon gives speed climbers a huge disadvantage. - The independence of irrelevant alternatives is violated, which is an issue of rank-product scoring. - Solution: 1 set of medals for speed and 1 set of medals for bouldering and lead. - It is confirmed that at Paris 2024, there will be 2 sets of medals: - Lead and bouldering, combined - Speed-only event --- # Acknowledgements .pull-left[ <img src="data:image/png;base64,#hannah.png" width="67%" style="display: block; margin: auto auto auto 0;" /> Hannah Butler <br>Colorado State University ] .pull-right[  Gregory J. Matthews <br>Loyola University Chicago ] --- # How it started .pull-left[ <blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/qntkhvn?ref_src=twsrc%5Etfw">@qntkhvn</a> Yo. I have an idea for a quick paper. We could probably write it up as a note in like a week. It's about the scoring system in sport climbing. Any interest?</p>— Volume Tweeter (@StatsInTheWild) <a href="https://twitter.com/StatsInTheWild/status/1411033054890500096?ref_src=twsrc%5Etfw">July 2, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> ] .pull-right[ <img src="data:image/png;base64,#blog.png" width="90%" style="display: block; margin: auto;" /> ] --- # UCSAS 2021 <center> <blockquote class="twitter-tweet"><p lang="en" dir="ltr"><a href="https://twitter.com/hashtag/UCSAS2021?src=hash&ref_src=twsrc%5Etfw">#UCSAS2021</a> poster on sport climbing's combined competition format and rank-product scoring system, joint work with @neighboringCity and <a href="https://twitter.com/StatsInTheWild?ref_src=twsrc%5Etfw">@StatsInTheWild</a>. <br><br>GitHub: <a href="https://t.co/Omq7v52lbr">https://t.co/Omq7v52lbr</a><br>Series of climbing blog posts: <a href="https://t.co/FRjJS14Bqw">https://t.co/FRjJS14Bqw</a><a href="https://twitter.com/hashtag/RStats?src=hash&ref_src=twsrc%5Etfw">#RStats</a> <a href="https://twitter.com/hashtag/sportsanalytics?src=hash&ref_src=twsrc%5Etfw">#sportsanalytics</a> <a href="https://t.co/t9G0PKzLh0">pic.twitter.com/t9G0PKzLh0</a></p>— qntkhvn (@qntkhvn) <a href="https://twitter.com/qntkhvn/status/1445765942969978888?ref_src=twsrc%5Etfw">October 6, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script> </center> --- # Related links <!-- ####
[nminhquang.99@gmail.com](mailto:nminhquang.99@gmail.com) --> <!-- ####
[@qntkhvn](https://twitter.com/qntkhvn) -->
**[github.com/qntkhvn/climbing](https://github.com/qntkhvn/climbing)**
**[doi.org/10.6339/22-JDS1042](https://doi.org/10.6339/22-JDS1042)**
**[bit.ly/3lrnzlD](https://bit.ly/3lrnzlD)** <center> <big> Cheers. </big> </centeR> <!-- #### Slides created via the `R` packages [**`xaringan`**](https://github.com/yihui/xaringan) and [**`xaringanthemer`**](https://github.com/gadenbuie/xaringanthemer). -->